Jan Mikusiński (April 3, 1913 Stanisławów – July 27, 1987

Katowice Katowice ( , , ; szl, Katowicy; german: Kattowitz, yi, קאַטעוויץ, Kattevitz) is the capital city of the Silesian Voivodeship in southern Poland and the central city of the Upper Silesian metropolitan area. It is the 11th most popul ...

) was a Polish mathematician based at the

University of Wrocław , ''Schlesische Friedrich-Wilhelms-Universität zu Breslau'' (before 1945) , free_label = Specialty programs , free = , colors = Blue , website uni.wroc.pl The University of Wrocław ( pl, Uniwersytet Wrocławski, U ...

known for his pioneering work in

mathematical analysis Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (m ...

. Mikusiński developed an

operational calculus Operational calculus, also known as operational analysis, is a technique by which problems in analysis, in particular differential equations, are transformed into algebraic problems, usually the problem of solving a polynomial equation. History Th ...

– known as the ''Calculus of Mikusiński'' ( MSC 44A40), which is relevant for solving

differential equations In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...

. His operational calculus is based upon an

algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary a ...

of the convolution of functions with respect to the

Fourier transform A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, ...

. From the convolution product he goes on to define what in other contexts is called the

field of fractions In abstract algebra, the field of fractions of an integral domain is the smallest field in which it can be embedded. The construction of the field of fractions is modeled on the relationship between the integral domain of integers and the field ...

or a quotient field. These ordered pairs of functions Mikusiński calls "operators", the "Mikusiński operators". He is also well known for Mikusinski's cube, the Antosik–Mikusinski theorem, and Mikusinski convolution algebra. A street in

is named after Mikusiński.

Selected publications

* ''An Introduction to Analysis - From Number to Integral.'' Wiley 1993 * ''The Operational Calculus.'' Pergamon Press, Oxford 1983 * ''Operatorenrechnung.'' VEB Deutscher Verlag der Wissenschaften, Berlin 1957. * ''The Bochner Integral.'' Birkhäuser 1978. * with Piotr Antosik,

Roman Sikorski Roman Sikorski (July 11, 1920 – September 12, 1983) was a Polish mathematician. Biography Sikorski was a professor at the University of Warsaw from 1952 until 1982. Since 1962, he was a member of the Polish Academy of Sciences. Sikorski's ...

: ''Theory of distributions – the sequential approach.'' Elsevier 1973. * with Stanisław Hartman: ''The theory of Lebesgue Measure and Integration.'' Pergamon Press, Oxford 1961.

External links

Caricature of Jan Mikusinski

Rachunek Operatorow
(1944)(Operational Calculus ''in Polish'')
Part 1

Part 2
1983 (English)

* {{DEFAULTSORT:Mikusinski, Jan 1913 births 1987 deaths 20th-century Polish mathematicians Recipients of the State Award Badge (Poland) People from Ivano-Frankivsk

Selected publications

See also

External links